Next Number

Can you find the next number in the below sequence
3 , 7 , 10 , 11 , 12 , 17 ?




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If we tie a Sheep to one peg, a circled grass is been eaten by the Sheep. If we tie the Sheep to two pegs with a circle on its neck, then an eclipse is eaten out of the grass by the Sheep. If we want an eclipse then we put two pegs and then put a rope in between them and the other end of the rope is tied up on the Sheep's neck.

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Challenging

There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.